Excitation of the higher-order HEM12d mode in a cylindrical dielectric resonator antenna (CDRA) was a big challenge, which was recently resolved by the present authors, nearly 30 years after the invention of the dielectric resonator antenna (DRA). Significantly, the radiation characteristics of this mode closely follow those due to the HEM11d mode, but with relatively higher gain. This breakthrough was made possible by introducing a new concept of feeding, and this was experimentally verified using a single prototype. Here, we have thoroughly investigated the design opportunities and limitations in terms of the material properties and dielectric resonator antenna's dimensions. Based on acquired knowledge, a comprehensive design guideline is provided to facilitate future designers estimating the best possible configuration for any specified application. As a significant part of this, the feed design has also been addressed. For practical verification, a customized dielectric resonator antenna was fabricated and measured, indicating excellent agreement with the proposed guidelines. © 2014 IEEE.